A conventional power supply device is shown in Japanese Patent Laid-Open 60 (1985) - 144730. This power supply device has a main battery and a backup battery. While the ignition switch is on, the main battery supplies power to automotive electric appliances. When the ignition switch is off, the backup battery supplies power. The backup battery is charged by the main battery. In this power supply device, if the charged power in the backup battery drops when the ignition switch is off, the power supplied to the automotive electric appliances decreases, and therefore the appliances may not work properly. If the power drops to a very low level, the memory of an appliance may lose its stored information.